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Advanced Engineering Mathematics with MATLAB 5th Edition by Dean G. Duffy, ISBN-13: 978-0367624057

Name: Advanced Engineering Mathematics with MATLAB 5th Edition by Dean G. Duffy, ISBN-13: 978-0367624057
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Category: Mathematics Tags: Advanced Engineering Mathematics with MATLAB 5th Edition by Dean G. Duffy, Dean G. Duffy, ISBN-10: 0367624052, ISBN-13: 978-0367624057 Product ID: 87035

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Advanced Engineering Mathematics with MATLAB 5th Edition by Dean G. Duffy, ISBN-13: 978-0367624057

[PDF eBook eTextbook]

Publisher: ‎ Chapman and Hall/CRC; 5th edition (December 31, 2021)
Language: ‎ English
‎616 pages
ISBN-10: ‎ 0367624052
ISBN-13: ‎ 978-0367624057

In the four previous editions the author presented a text firmly grounded in the mathematics that engineers and scientists must understand and know how to use. Tapping into decades of teaching at the US Navy Academy and the US Military Academy and serving for twenty-five years at (NASA) Goddard Space Flight, he combines a teaching and practical experience that is rare among authors of advanced engineering mathematics books.

This edition offers a smaller, easier to read, and useful version of this classic textbook. While competing textbooks continue to grow, the book presents a slimmer, more concise option. Instructors and students alike are rejecting the encyclopedic tome with its higher and higher price aimed at undergraduates.

To assist in the choice of topics included in this new edition, the author reviewed the syllabi of various engineering mathematics courses that are taught at a wide variety of schools. Due to time constraints an instructor can select perhaps three to four topics from the book, the most likely being ordinary differential equations, Laplace transforms, Fourier series and separation of variables to solve the wave, heat, or Laplace’s equation. Laplace transforms are occasionally replaced by linear algebra or vector calculus.

Sturm-Liouville problem and special functions (Legendre and Bessel functions) are included for completeness. Topics such as z-transforms and complex variables are now offered in a companion book, Advanced Engineering Mathematics: A Second Course by the same author.

MATLAB is still employed to reinforce the concepts that are taught. Of course, this Edition continues to offer a wealth of examples and applications from the scientific and engineering literature, a highlight of previous editions. Worked solutions are given in the back of the book.

Table of Contents:

Dedication

Contents

vii

Acknowledgments

xiii

Author

Introduction

xvii

ListofDefinitions

xix

Chapter1:

First-OrderOrdinary

DifferentialEquations

1.1ClassificationofDifferentialEquations

1.2SeparationofVariables

1.3HomogeneousEquations

1.4ExactEquations

1.5LinearEquations

vii

1.6GraphicalSolutions

1.7NumericalMethods

Chapter2:

Higher-OrderOrdinary

Differential Equations

2.1HomogeneousLinearEquationswithConstantCoefficients

2.2SimpleHarmonicMotion

2.3DampedHarmonicMotion

2.4MethodofUndeterminedCoefficients

2.5ForcedHarmonicMotion

2.6VariationofParameters

2.7Euler-CauchyEquation

2.8PhaseDiagrams

2.9NumericalMethods

Chapter3:Linear Algebra

101

3.1Fundamentals

101

3.2Determinants

109

3.3Cramer’sRule

113

3.4RowEchelonFormandGaussianElimination

115

3.5EigenvaluesandEigenvectors

129

3.6SystemsofLinearDifferentialEquations

136

3.7MatrixExponential

141

TableofContents ix

Chapter4:VectorCalculus1474.1Review1474.2DivergenceandCurl1544.3LineIntegrals1584.4ThePotentialFunction1634.5SurfaceIntegrals1644.6Green’sLemma1714.7Stokes’Theorem1744.8DivergenceTheorem181Chapter5:FourierSeries1895.1FourierSeries1905.2PropertiesofFourierSeries2025.3Half-RangeExpansions2115.4FourierSerieswithPhaseAngles2165.5ComplexFourierSeries2205.6TheUseofFourierSeriesintheSolutionofOrdinaryDifferentialEquations2255.7FiniteFourierSeries232Chapter6:TheFourierTransform2496.1FourierTransforms2496.2FourierTransformsContainingtheDeltaFunction262

6.3

PropertiesofFourierTransforms

264

6.4

InversionofFourierTransforms

275

6.5

Convolution

279

6.6

TheSolutionofOrdinaryDifferentialEquationsbyFourierTransforms

283

6.7

TheSolutionofLaplace’sEquationontheUpperHalf-Plane

285

6.8

TheSolutionoftheHeatEquation

287

Chapter7:

TheLaplaceTransform

295

7.1

DefinitionandElementaryProperties

295

7.2

TheHeavisideStepandDiracDeltaFunctions

299

7.3

SomeUsefulTheorems

307

7.4

TheLaplaceTransformofaPeriodicFunction

315

7.5

InversionbyPartialFractions:Heaviside’sExpansionTheorem

317

7.6

Convolution

324

7.7

SolutionofLinearDifferentialEquationswithConstantCoefficients

329

Chapter8:

TheWaveEquation

347

8.1

TheVibratingString

348

8.2

InitialConditions:CauchyProblem

351

8.3

SeparationofVariables

351

8.4

D’Alembert’sFormula

365

8.5

NumericalSolutionoftheWaveEquation

372

Chapter9:TheHeatEquation3879.1DerivationoftheHeatEquation3879.2InitialandBoundaryConditions3899.3SeparationofVariables3909.4TheSuperpositionIntegral4059.5NumericalSolutionoftheHeatEquation409

Chapter10:Laplace’sEquation41910.1DerivationofLaplace’sEquation41910.2BoundaryConditions42110.3SeparationofVariables42210.4Poisson’sEquationonaRectangle42910.5NumericalSolutionofLaplace’sEquation433

Chapter11:TheSturm-LiouvilleProblem44311.1EigenvaluesandEigenfunctions44411.2OrthogonalityofEigenfunctions45711.3ExpansioninSeriesofEigenfunctions46111.4FiniteElementMethod485

Chapter12:

SpecialFunctions493

12.1LegendrePolynomials495

12.2BesselFunctions519

12.AAppendixA:DerivationoftheLaplacianinPolarCoordinates567

12.BAppendixB:DerivationoftheLaplacianinSphericalPolarCoordinates568

AnswerstotheOdd-NumberedProblems571

Index589

Dean G. Duffy is a former mathematics instructor at the US Naval Academy and US Military Academy. He spent 25 years working on numerical weather prediction, oceanic wave modeling, and dynamical meteorology at NASA’s Goddard Space Flight Center. Prior to this, he was a numerical weather prediction officer in the US Air Force. He earned his Ph.D. in meteorology from MIT. Dr. Duffy has written several books on transform methods, engineering mathematics, and mixed boundary value problems including Green’s Functions with Applications, Second Edition, published by CRC Press.

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